Объяснение:
1)2(1-sin^2 4x/3)+11sin 4x/3-7=0
2-2sin^2 4x/3+11sin 4x/3-7=0
2sin^2 4x/3-11 sin 4x/3+5=0
Пусть sin 4x/3=x
2x^2-11x+5=0
D=121-4•2•5=121-40=81
x1=(11+9)/4=5(н.з)
x2=(11-9)/4=1/2
sin 4x/3=1/2
4x/3=(-1)^n•п/6+пn
x=(-1)^n•п/8+3пn/4
2)3cos8x-cos4x+1=0
3(2cos^2 4x-1)-cos4x+1=0
6cos^2 4x-3-cos4x+1=0
6cos^2 4x-cos4x-2=0
Пусть cos4x=x
6x^2-x-2=0
D=1-4•6•(-2)=49
x1=(1+7)/12=2/3
x2=(1-7)/12=-1/2
cos 4x=2/3
4x=+-arccos2/3+2пn
x=+-1/4arccos2/3+пn/2
cos 4x=-1/2
4x=+-2п/3+2пn
x=+-п/6+пn/2
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Answers & Comments
Объяснение:
1)2(1-sin^2 4x/3)+11sin 4x/3-7=0
2-2sin^2 4x/3+11sin 4x/3-7=0
2sin^2 4x/3-11 sin 4x/3+5=0
Пусть sin 4x/3=x
2x^2-11x+5=0
D=121-4•2•5=121-40=81
x1=(11+9)/4=5(н.з)
x2=(11-9)/4=1/2
sin 4x/3=1/2
4x/3=(-1)^n•п/6+пn
x=(-1)^n•п/8+3пn/4
2)3cos8x-cos4x+1=0
3(2cos^2 4x-1)-cos4x+1=0
6cos^2 4x-3-cos4x+1=0
6cos^2 4x-cos4x-2=0
Пусть cos4x=x
6x^2-x-2=0
D=1-4•6•(-2)=49
x1=(1+7)/12=2/3
x2=(1-7)/12=-1/2
cos 4x=2/3
4x=+-arccos2/3+2пn
x=+-1/4arccos2/3+пn/2
cos 4x=-1/2
4x=+-2п/3+2пn
x=+-п/6+пn/2